MOTECC : 1991. - GBV · Second Order MCSCFEquation 258 Orbital Gradient 259 ... Restricted-step,...

Modern Techniquesin

Computational Chemistry:MOTECC-91

Edited by

Enrico Ciementi

International Business Machines Corporation

Kingston, New York 12401, U.S.A.

ESCOM

Leiden 1991

Contents

Foreword to MOTECC-91 v

Foreword to MOTECC-90 vii

Foreword to MOTECC-89 xi

Chapter 1. Introduction to MOTECC-91

E. Ciementi

IBM Corporation, Dept. 48BJ428, Neighborhood Road

Kingston, NY 12401, USA

Introduction 1

Evolution of Computers and Simulations 2

Global Simulation 9

MOTECC-91: An "Assembly Line" to Produce Chemical Information....

12

An Example of Global Simulation: From 3 Nuclei and 10 Electrons

to a Million Molecules 17

Conclusions 20

References 20

Chapter 2. Independent Electron Models: Hartree-Fock for

Many-Electron Atoms

E. Ciementi, S.J. Chakravorty, G. Corongiu, J.R. Flores

and V. Sonnad



Introduction and Chapter Organization 23

The Analytic Hartree-Fock Method 26

Open Shell Methods and Roothaan Vector Coupling Coefficients 31

Basis Sets for Atomic Computations 34

Optimization of Orbital Exponents 43

Contraction Coefficients 44

Geometrical Basis Sets 46

Matrix Elements, Spherical Symmetry and Integrals 61

xv

xvj Contents

The Correlation and Pair Correlation Energies 67

Density Functional for Atomic Computations 79

Configuration and Momentum Expectation Values 90

The Finite Element Method (FEM) 93

Appendix 2A. Two-Electron Integrals 107

Appendix 2B. Pseudopotentials 109

References 110

Chapter 3. Non-Relativistic Configuration Interaction Calculations

for Many-Electron Atoms: ATOMCI

F. Sasaki, M. Sekiya, T. Noro, K. Ohtsuki and Y. Osanai

Department of Chemistry, Faculty of Science, Hokkaido University

Sapporo 060, Japan

Introduction 115

Tensor Operator 117

Recoupling Transformation 121

Complete Set of Shell States 125

Shell Creation Tensor Operators in LS-scheme 126

Complete Shell States in LSQ-scheme 131

Generation of Shell States in ATOMCI 138

Matrix Elements 138

Orthonormal Tensors for Many Shells 138

Hamiltonian Operator 141

Reduction Formulas for Matrix Elements 142

Appendix 3A. Simply Reducible Group 146

Integer Representation and Half Integer Representation 147

Even and Odd Representation 150

Three-j Symbols 153

Six-j Symbol and Nine-j Symbol 159

Appendix 3B. Rotation Group 164

References 166

Chapter 4. Kinetically Balanced Geometric Gaussian Basis Set Calculations

for Relativistic Many-Electron Atoms

A.K. Mohanty, F.A. Parpia and E. Ciementi

IBM Corporation, Dept. 48B/428, Neighborhood Road


Introduction 167

Relativistic Hamiltonians and Relativistic Orbitals 169

Matrix Elements of the Hamiltonian 171

Choice of Basis Sets 174Relativistic Hartree-Fock-Roothaan Equation 175Angular Coefficients 177

Contents xvii

Evaluation of Radial Integrals 180

Finite Nucleus Approximation 182

Open-Shell Calculations 184

Vector Coupling Coefficients 189

Dirac-Fock Calculations 193

Dirac-Fock-Breit Calculations 200

Conclusions 204

References 206

Chapter 5. A Relativistic Mulriconflguration Self-Consistent-Field

Method for Atoms

F.A. Parpia and A.K. MohantyIBM Corporation, Dept. 48B/428, Neighborhood Road


Introduction 211

Relativistic Hamiltonians 212

Relativistic Wavefunctions 213

The Hamiltonian Matrix 216

Approximate Atomic Energies 217

The Energy Functional 218

Relativistic Basis Set Methods 218

Relativistic Gaussian Basis Sets 222

Analytical Expressions for One Electron Integrals 223

Analytical Expressions for Two Electron Integrals 226

The Method of Rotations 227

Conclusion 229

References 229

Chapter 6. ALCHEMY II: A Research Tool for Molecular Electronic

Structure and Interactions

A.D. McLean, M.Yoshimine, B.H. Lengsfield,P.S. Bagus and B. Liu

IBM Research Division, Almaden Research Center

650 Harry Road, San Jose, CA 95120-6099, USA

Introduction 233

ALCHEMY II Program Modules 234

Weak Molecular Interactions 236

The He - H20 Interaction 241

Approximate ICF Configuration Spaces 249

xvj;jContents

Appendix 6A. The MOLECULE Integral Generator254

J. Almlbf

Dept. of Chemistry, University of Minnesota

Minneapolis, MN 55455, USA

P.R. TaylorFLORET Institute, Palo Alto, CA 94303, USA

NASA Ames Research Center, Moffet Field, CA 94035, USA

Appendix 6B. Algorithm for Large Scale Second Order

MCSCF Calculations 256

B. Liu and B.H. LengsfieldIBM Research Division, Almaden Research Center,

650 Harry Road, San Jose, CA 95120-6099, USA

Introduction 256

Overview of the MCSCF Method 257

Second Order MCSCF Equation 258

Orbital Gradient 259

CI Gradient 259

Orbital Hessian 260

CI-Orbital Coupling 261

CI Hessian 261

Large CI Expansions 261

Matrix Formulation of Orbital Hessian 263

Orbital Hessian 263

Integral Transformation 265

Iterative Solution of MCSCF Equations 266

Iterative Solution of a System of Linear Equations 267

Convergence Threshold 268

The CI Portion of VX 269

The Prototype CI Method 269

Overview 269

Prototype Configurations 270

Prototype Matrices 272

Prototype Diagonal Matrices 273

Prototype Singles Matrices 274

Prototype Doubles Matrices 274

Discussion 275

References 276

Chapter 7. Quantum Molecular Dynamics with Gaussian Basis Set

B. Feuston, C. Lee and E. Ciementi



Contents xix

Introduction 279

Combined DFT-MD Approach 280

DFT with LCAO-Contracted Gaussians as a Basis Set 283

Solutions to the Kohn-Sham Equations 286

Energy Gradients and Molecular Dynamics 289

Geometry Optimization 289

Molecular Dynamics 290

Example Calculation 291

Summary 292

References 293

Chapter 8. Molecular Interactions and Large Molecules with KGNMOL

E. Ciementi, G. Corongiu and O.G. Stradella



Introduction 295

Computation of Carbon Clusters 297

Basis Sets: Gaussian Type Functions 307

The Hydrogen Molecule and the Water Dirner 310

Basis Set Superposition Error (BSSE) 316

Special Options for Adding Fragments or Molecules: ADD Option 317

The MP2 Option 319

Density Functionals for Molecules 321

Clementi-Chakravorty Electron-Pair Functional 334

Topology of Molecular Charge Distributions 339

One-Electron Integral Formulae 341

Incomplete and Complete Gamma Function 341

Product of Gaussian Type Functions 345

Normalization of Gaussian Type Functions 346

Two-Electron Integral Formulae 349

General Analytical Formulae 349

Special Formulas for Integrals Involving s- and p-Type Functions 352

Two-Electron Integrals with Explicit Factorization of the

One-Electron Dependent Terms 356

Geometrical Basis Sets and Their Use 358

Effective Core Potentials 366

Packing and Unpacking Routines for Storing Two-Electron Integralsand Indices 367

Appendix 8A. The Gaussian Product Theorem 370

Appendix 8B. Integrals Related to the Gamma Function 372

References 374

xxContents

Chapter 9. MELD: A Many Electron Description

E.R. Davidson

Department of Chemistry, Indiana University

Bloomington, IN 47405, USA

Introduction 381

Integrals382

One-Electron Integrals, Closed Form 386

Other One-Electron Integrals 387

Two-Electron Integrals389

Auxiliary Functions 391

Charge Distributions 394

Pseudo Potentials 394

Symmetrized Integrals 405

Self Consistent Field 408

Integral Transformation 412

Configuration Interaction 413

Eigenvalue Program 415

Molecular Properties 418

Appendix 9A. Evaluation of CI Matrix Elements 419

References 433

Chapter 10. MOLCAS: A General Purpose Quantum Chemistry Program

System for Correlated Wavefunctions

B.O. Roos, G. Karlstrom, P.-A. Malmqvist, A.J. Sadlej

Department of Theoretical Chemistry, Chemical Centre

P.O.B. 124, S-221 00 Lund, Sweden

P.-O. Widmark

S&TC Group, ACIS, IBM Sweden

Introduction 435

Program Descriptions 437

Integral Evaluation and Handling 437

The Two-Electron Transformation Program MOTRA 439

The Self Consistent Field (SCF) Program 440

The Restricted Active Space (RAS) SCF Program 441

The RAS State Interaction (RASSI) Program 444

The Configuration Interaction Programs 446

Many Body Perturbation Theory (MBPT) Programs 448

The Molecular Properties Program 449

A Timing Example, The Pyrimidine Molecule 450

Concluding Remarks 452

References 453

Contents xxi

Chapter 11. AMPAC: A General Program for Chemical Calculations UsingProcedures Developed by the Dewar Group

Michael J.S. Dewar

Department of Chemistry, The University of Florida

Gainesville, FL 32611, USA

Introduction 455

Theory 458

Applications of AMPAC 461

Accuracy 463

MOPAC and PM3 464

References 466

Chapter 12. HONDO: A General Atomic and Molecular Electronic

Structure System

M. Dupuis and S.A. Maluendes

IBM Corporation, Dept. 41PA/428, Neighborhood Road


Introduction 469

Wavefunctions and Energies 470

Closed Shell Hartree-Fock (SCF) Wavefunction 470

Spin Unrestricted Open Shell Hartree-Fock (UHF) Wavefunction 477

High Spin Restricted Open Shell Hartree-Fock (ROHF)Wavefunction 478

General Restricted Open Shell Hartree-Fock and Generalized

Valence Bond Wavefunctions (ROHF-GVB) 479

Configuration Interaction (CI) Wavefunction 480

Multiconfiguration Hartree-Fock (MCSCF) Wavefunction 481

Moller-Plesset Perturbation (MP2, MP3, MP4) 486

Electronic Properties 506

Dipole Polarizability and Hyperpolarizabilities 507

Molecular Structure Options 512

Equilibrium Structure Determination 512

Transition State Determination 513

Force Constant Calculation 513

Infrared and Raman Intensities Calculation 513

Reaction Pathway Determination 514

Potential Surface Scan 515

Crossing Seam Minimum Energy Point Determination 515

Non-Gradient Optimization 516

Other Options 516

Electron Transfer Reactions 516

Effective Core Potentials 521

Representation of An External Field 521

Miscellaneous Features 521

xx;j Contents

Integrals and Derivatives 521

Point Group Symmetry -524

Illustrative Examples 528

References -531

Chapter 13. HYCOIN: Hylleraas Configuration Interaction Method UsingGaussian Functions

A. Preiskorn, D. Frye, G.C. Lie and E. Ciementi



Introduction 535

HCI Theory 538

Applications and Specific Examples 542

Two-electron Systems 542

Verification of the Three-Electron Theory 544

Two-electron Integrals in Gaussian Cartesian Functions 546

The S Integral 547

The K Integral 548

The N Integral 549

Three-electron Integrals in Gaussian Cartesian Functions 551

The S Integral 552

The T Integral 554

The K Integral 557

The N Integral 557

Four-electron Integrals in Gaussian Cartesian Functions 560

The S Integral 561

The T Integral 564

The U Integral 565

Many-electron Integrals in Gaussian Lobe Functions 567

Two-electron Integral Formulas 569The K Integral 570The S Integral 571The N Integral 571

Three-electron Integral Formulas 572

The K Integral 572

The S Integrals 573

The T Integral 578The N Integral 580

Numerical Examples and Discussion 587

Many-electron Integrals with Exponential-type Correlation Factor 588

The SE Integral 589

The EE Integral 590

The KE Integral 591

The NE Integral 592

Contents xxjjj

Appendix 13A. The R(rj) Operator 594

References 595

Chapter 14. SIRIUS: A General Purpose Direct Second Order MCSCF

Program

H.J.Aa. Jensen

Department of Chemistry, University of Aarhus

DK-8000 Aarhus C, Denmark

H. AgrenInstitute of Quantum Chemistry, University of UppsalaBox 518, S-751 20 Uppsala, Sweden

J. Olsen

Theoretical Chemistry, Chemistry Center, University ofLund

Box 124, S-221 00 Lund, Sweden

Introduction 599

Outline of Program Features 600

Theory 603

Orbital Based Quantum Chemistry: The Hamiltonian 603

Parameterization of the MCSCF Wave Functions 604

Restricted-step, Second-order MCSCF Optimization 608

The Direct Iterative NEO Algorithm 611

Implementation 615

Gradient Evaluation 617

The Macro Iterations, Step Calculation, and Step Control 619

The Micro Iterations, the Dynamical Update of the Damping Factor,and the Direct MCSCF Step 621

Integral Transformations 622

Step-Control Algorithm 623

Direct Configuration Interaction Theory 624

RAS-CI Expansions in a CSF Basis 624

Slater Determinants and Strings 628

Direct CI for RAS Expansions 631

Construction of Density Matrices 634

Counter Rotations of CI Coefficients 636

Auxiliary Optimization Algorithms 636

Split Configuration and Orbital Trial Vectors 636

Optimal Orbital Trial Vectors 638

Convergence of Solution Vectors in Direct NEO and NR Algorithms . . .639

Transformation to Natural and Fock Type Orbitals 641

Intermediate Optimization of Orbitals for Fixed ConfigurationCoefficients 641

Initial Guess and Optimization of Core Hole States 643

References 644

xxjvContents

Chapter 15. Dirac-Fock Self-Consistent Field Calculations for Closed

Shell Molecules with Kinetic Balance and Finite Nuclear Size

A. Mohanty, S. Panigrahy and E. Ciementi



Introduction647

Preliminary650

Choice of Basis Spinors656

Evaluation of One-Electron and Two-Electron Matrix Elements 660

Evaluation of Small-Component Matrix Elements 664

Evaluation of Primitive Integrals in Cartesian Form 673

Numerical Considerations and Preliminary Results 678


Appendix 15A. Finite Nuclear Size Corrections 683

Appendix 15B. Eulerian Angles and Rotation Matrix Elements 688

References 691

Chapter 16. Continuum by L2 Methods: Molecular Photoionization

Cross Section

/. Cacelli

Scuola Normale Superiore, Piazza dei Cavalieri, 56126 Pisa, Italy

V. Carravetta and A. Rizzo

I. C. Q. E. M. del CNR, Via Risorgimento 35, 56126 Pisa, Italy

R. Moccia

Dipartimento di Chimica e Chimica Industriale, Universita di Pisa

Via Risorgimento 35, 56126 Pisa, Italy

Introduction 695

Molecular States in the Electronic Continuum 697

The K-Matrix Technique 700

The Partial Wave Channels 700

The L2 Basis Set Approximation 705

RPA Matrix Elements in the Continuum 708

One- and Two-Photons Transition Matrix Elements 710

One-Photon Transitions 710

Two-Photon Transitions 712

Integral Cross Section by L2 Methods 717

Stieltjes Imaging 718

Generalization of the Stieltjes Imaging 721

Computational Aspects 723

The Basis Set 723

One Photon Ionization 731

Two Photon Ionization 736

Contents xxv

Appendix 16A. Rotationally Averaged Differential Cross Sections 741

References 745

Chapter 17. RMPROP: A Computer Program for Quantum Mechanical Close

Coupling Calculations for Inelastic Collisions

M.J. Unekis, D.W. Schwenke*, N. Mullaney Harvey,and D.G. Truhlar

Dept. of Chemistry, Chemical Physics Program, and

Supercomputer Institute, University of Minnesota

Minneapolis, MN 55455-0431, USA

* University of Minnesota and NASA Ames Research Center

Moffett Field, CA 94035, USA

Introduction 749

Close Coupling Theory 751

Coupled Channels Equations 751

Asymptotic Boundary Conditions 754

R Matrix Propagation Algorithm 756

Sector Adiabatic Basis Functions 756

Sector Propagation Matrix 757

Stepsize Determination 760

Propagation Across Sector Boundaries 761

Reduction of the Number of Closed Channels Propagated in the

Large-r Region 762

Asymptotic Reordering of Channels 764

Single and Multiple Energy Runs 767

Program Structure 768

Segmentation of Program and Flow Chart 768

Restart Options 769

Vectorization 771


References 772

Chapter 18. BNDPKG2: A Linear Combination of Gaussian Orbitals (LCGO)

Band Structure Program for Cubic Crystals with One Atom

per Unit Cell

N.E. Brener and J. CallawayDepartment of Physics and Astronomy

Louisiana State University, Baton Rouge, LA 70803, USA

J.M. Tyler

Department of Computer Science

Louisiana State University, Baton Rouge, LA 70803, USA

Introduction 773

The LCGO Method for Energy Band Calculations 775

xxvj Contents

BNDPKG 2 779

Sample BNDPKG 2 Calculations 785

References 790

Chapter 19. LCAO Ab Initio Band Structure Calculations for Polymers

J.M. Andre, J.L. Bredas, J. Delhalle and J.G. Fripiat

Laboratoire de Chimie Theorique Appliquee

Facultes Universitaires Notre-Dame de la Paix, 61 rue de Bruxelles

B-5000 Namur, Belgium

D.J. Vanderveken and D.P. Vercauteren

Laboratoire de Chimie Moleculaire Structurale

Facultes Universitaires Notre-Dame de la Paix, 61 rue de Bruxelles

B-5000 Namur, Belgium

Introduction 793

The Periodic Model of a Polymer Chain 794

Principles of LCAO Band Structure Calculations on Polymers 797

The Electrostatic Balance between the Nucleus- and

Electron-Electron Interactions 803

Multipole Expansion for Long-Range Coulomb Interactions 807

The Short- or Long-Rangeness Character of the ExchangeContribution 809

Use of Screw Symmetry in Polymer Calculations 811

A Simulated Ab Initio Technique: The Valence Effective

Hamiltonian (VEH) 813

Particular Aspects of Computer Implementation 816

Band Structure Calculations 816

Summation over Polymeric States and Integrations over

First Brillouin Zones 816

Basis Set Linear Dependence 817

Band Indexing Difficulty 819

Density of States Calculations 821

Graphics Interface: BandDos 822

Applications 826

Appendix 19A. Tables of VEH Parameters 826

Single-Zeta Potentials 826

Double-Zeta Potentials 826

References 828

Chapter 20. First Principles Molecular Dynamics

M. Parrinello

IBM Research Division, Zurich Research LaboratoryCH-8803 Ruschlikon, Switzerland

Introduction 833

The Interatomic Potential within DF Theory 835

A Dynamical Approach to Energy Functional Minimization 837

Molecular Dynamics in the Coupled Electron-Ion Parameter Space 840

Conclusions 844

References 845

Chapter 21. Molecular Dynamics Simulations with ab initio

Interaction Potentials

G. Corongiu, M. Aida, M.F. Pas, and E. Ciementi

IBM Corporation, Dept. 48B\428, Neighborhood Road


Introduction 847

Interaction Potentials 848

Ab initio Force Field for Biomolecules 850

Classification of Atoms 851

The Molecular Dynamics Method 857

Numerical Integration for the Equations ofMotion 859

Calculation of Properties 862

Properties Related to Neutron Scattering Experiments 868

Periodic Boundary Conditions and Long Range Forces 876

Free Energy Calculations 878

Energy Minimization 882

Gradient Methods 883

Minimization Applications 885

Applications and Examples 889

Liquid Water with the Flexible ab initio Potential 889

BPTI Simulations in Vacuo and in Solution 902

Neutron Scattering Properties 905

Examples Using the ab initio Force Field 908

a-Helix Stability of C-peptide 908

Conformational Analysis of Cyclolinopeptide A 910

Interaction of Spermine with Oligonucleotide 913

References

xxviii Contents

Chapter 22. Langevin Dynamics Simulations of Biomolecules

D.K. Bhattacharya, W. Xue and E. Ciementi



Introduction 921

Computational Algorithm for Langevin Dynamics Simulations 922

Langevin Dynamics Simulation of the BPTI Protein 927

Discussion 935

References 937

Chapter 23. Molecular Dynamics Simulations of Fluid Flows

D.K. Bhattacharya, G. C. Lie and E. Ciementi



Introduction 939

Computational Algorithm for a Large Scale Molecular DynamicsSimulation 942

Applications and a Discussion of Results 946

References 968

Chapter 24. Brownian Dynamics Simulations of a Complex Fluid System

D.K. Bhattacharya and E. Ciementi



Introduction 971

Brownian Dynamics Simulation: Basic Concepts 973

Fokker-Planck Description 973

Langevin Description 975

The Simulation Program "BROWNIAN": An Overview 979

The Nonlinear Rheology of the Colloidal Suspension 980

Discussion 983

Shear Induced Phase Transition in a Colloidal Suspension 984

Generalized Brownian Dynamics Techniques 986

References 987

Chapter 25. Protein Structure Prediction and Neural Networks

/. Vanhala and E. Ciementi



Introduction 991

Neural Networks 993

Contents xxix

Neural Networks in Globular Protein Secondary Structure

Predictions 997

Neural Networks in Globular Protein Tertiary Structure

Predictions 999

Methods 999

Tools 1002

Testing the Proposal: BPTI as an Example 1006

Discussion and Future Development 1009

References 1011

Chapter 26. Cellular Automata

R. Panda, V. Sonnad and E. Ciementi



Cellular Automata 1017

Two-Dimensional Lattice-Gas Automata 1017

Simulation of 2D Fluid Flows 1021

Three-Dimensional Lattice-Gas Automata 1025

Results of 3D Simulations 1028

References 1029

Chapter 27. Microscopic and Mesoscopic Simulations of Complex Flows

with Cellular Automata and Related Techniques

S. Sued

IBM European Center for Scientific and Engineering ComputingVia Giorgione 159, 00147 Rome, Italy

R. Benzi

Dept. of Physics, Universitd di Roma II, Tor Vergata

Via O. Raimondo, 00173 Rome, Italy

A. Cancelliere

Dept. of Hydraulic Engineering, Universitd di Catania

Via A. Doria, Catania, Italy

F. Higuera

Dept. of Fluid Mechanics, School of Aeronautics

P.za Cardenal Cisneros, 28040 Madrid, Spain

M. VergassolaDept. of Physics, Universitd di Roma I, La SapienzaP.le Aldo Mow, 00185 Rome, Italy

Introduction 1031

Review of Boolean Lattice Gas 1032

From Microscopic to Mesoscopic: The Lattice Boltzmann Equation 1037

LBE with Enhanced Collisions 1038

xxx Contents

Subgrid Modelling of Fluid Turbulence 1042

Applications of LBE 1043

Three-dimensional Laminar Flows in Complex Geometries 1043

Bifurcations of a Two-dimensional Poiseuille Flow 1045

Fully Developed Two-dimensional Forced Turbulence 1046

Performance Considerations 1049

What Next? 1050

Quantum Automata 1051

Conclusion 1052

References 1053

Chapter 28. The Equations of Fluid Flow and Their Solution by

Numerical Methods

V. Sonnad, R. Panda, B. Jiang, H. Murakami,

S. Hassanzadeh and S. Foresti



The Equations of Fluid Flow 1055

Derivation of the Navier Stokes Equations 1055

Reduction to Various Specific Forms 1062

The Finite Element Method 1066

The Method of Weighted Residuals 1067

The H-Version of the Finite Element Method 1068

The P-Version of the Finite Element Method 1069

Solution Techniques 1070

Direct Solution Methods 1070

Iterative Methods 1071

Overview of Preconditioning Techniques 1072

Multilevel Solution Method 1073

Computational Solution of the Navier Stokes Equations 1075

Parallel Implementation of the Solution Scheme 1077

Turbulent Flow 1079

Reynolds Equations 1079

Empirical Relations for the Reynolds Stress Tensor 1081

Direct Numerical Simulation of Isotropic Turbulent Flows 1082

Dealiasing 1084

Time Stepping Scheme 1084

Parallel Implementation of the Numerical Scheme 1084

Results 1085

Application of the Finite Element Method in QuantumChemistry 1087

References 1088

Contents xxxi

Chapter 29. The Equations of Elasticity and Their Solution byFinite Element Methods

V. Sonnad, H. Murakami, S. Foresti, S. Hassanzadeh and B. JiangIBM Corporation, Dept. 48B/428, Neighborhood Road


The Equations of Elasticity 1091

Computational Techniques for Linear Static Analysis 1096

Solution of Large 3-D Problems with Finite Elements 1096

Iterative Solution with the Conjugate Gradient Method 1097

Rapid Operator Application 1098

Utility of Rapid Operator Application 1104

Parallel Implementation of Iterative Schemes 1104

References 1106

Chapter 30. Numerical Modeling of Axisymmetric Laminar Flames

M.D. Smooke

Dept. of Mechanical Engineering, Yale UniversityNew Haven, CT 06510, USA

Introduction 1109

Problem Formulation 1110

Method of Solution 1114

Serial Implementation 1114

Parallel Implementation 1115

References 1117

Chapter 31. Modeling of Atmospheric Pollutant Transport in Shorelines

Z.D. Christidis

IBM Research, T.J. Watson Research Center

Yorktown Heights, NY 10598, USA

P.J. Samson

Dept. of Atmospheric, Oceanic and Space Sciences

University of Michigan, Ann Arbor, MI 48109, USA

Introduction 1119

Model Development and Governing Equations 1120

Equations for the Mesoscale Variables 1122

Equations for the Synoptic Scale Variables 1123

Boundary Layer Parameterization 1124

Diffusivities in the Surface Layer 1124

Diffusivities in the Planetary Boundary Layer 1126

Numerical Methods 1127

Initial and Boundary Conditions 1128

Summertime Flow over a Lake 1131

xxxii Contents

Summary and Conclusions 1135

References 1137

Chapter 32. Interactive Visualization Techniques for Chemistry:

KGNGRAF, XWIB and REMOTE

S. Chin, M. Martins-Costa, R. Tagliavini, S.B. Rondeau

and J.P. Prost



Introduction 1139

The graPHIGS Application Programming Interface (API) 1140

Introduction to KGNGRAF 1143

The User Interface 1145

Display of Molecular Models 1146

Display of Electron Densities and Molecular Orbitals 1153

Creation and Manipulation of Molecules 1158

Superposition of Molecular Structures 1163

Molecule Building from Templates 1165

Protein Building from Templates 1166

Inquiry of Geometrical Parameters 1168

Display of Molecular Vibrations and Molecular Spectra 1168

Display of Molecular Energy Diagrams 1169

Interactive Animations 1169

Files Manipulation 1173

Windows Oriented Interfaces for Input Specification 1173

XWIB: An X Window Interface Builder 1178

Format Checking 1178

Dependency Handling Mechanisms 1178

Help Messages 1183

On-Line Documentation 1183

Other Utility Functions 1183

REMOTE: Remote File Transfer and Execution 1186

Summary '. 1188

References 1188

Contents xxxiii

Chapter 33. LCAP: Loosely Coupled Array of Processors Parallel

Processing Systems

E. Ciementi and S. Chin, G. Corongiu, J. Detrich, M. Dupuis,L.J. Evans, D. Folsom, D. Frye, G.C. Lie, D. Logan,D. Meek, V. Sonnad



Introduction 1191

The LCAP-3090 Experimental System 1193

Early LCAP Systems 1198

LCAP Parallel Processing Software and Performance Issues 1204

LCAP Design Philosophy 1207

LCAP Features for Effective Parallelism 1211

Conclusions 1219

Bibliography 1220

Author Index 1227

Subject Index 1251

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MOTECC : 1991. - GBV · Second Order MCSCFEquation 258 Orbital Gradient 259 ... Restricted-step,...

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Transcript of MOTECC : 1991. - GBV · Second Order MCSCFEquation 258 Orbital Gradient 259 ... Restricted-step,...